Editing Paraconsistent logic (section)

== Applications ==
Paraconsistent logic has been applied as a means of managing inconsistency in numerous domains, including:<ref name="See Bremer">Most of these are discussed in Bremer (2005) and Priest (2002).</ref>
* [[Semantics]]: Paraconsistent logic has been proposed as means of providing a simple and intuitive formal account of [[truth]] that does not fall prey to paradoxes such as [[Liar paradox|the Liar]]. However, such systems must also avoid [[Curry's paradox]], which is much more difficult as it does not essentially involve negation.
* [[Set theory]] and the [[foundations of mathematics]]
* [[Epistemology]] and [[belief revision]]: Paraconsistent logic has been proposed as a means of reasoning with and revising inconsistent theories and belief systems.
* [[Knowledge management]] and [[artificial intelligence]]: Some [[computer scientist]]s have utilized paraconsistent logic as a means of coping gracefully with inconsistent<ref>See, for example, [[truth maintenance systems]] or the articles in Bertossi et al. (2004).</ref> or contradictory<ref>Gershenson, C. (1999). Modelling emotions with multidimensional logic. In Proceedings of the 18th International Conference of the North American Fuzzy Information Processing Society (NAFIPS ’99), pp. 42–46, New York City, NY. IEEE Press. http://cogprints.org/1479/</ref> information. Mathematical framework and rules of paraconsistent logic have been proposed as the [[activation function]] of an [[artificial neuron]] in order to build a [[neural network]] for [[function approximation]], [[model identification]], and [[Control (management)|control]] with success.<ref>{{Cite journal|last1=de Carvalho Junior|first1=A.|last2=Justo|first2=J. F.|last3=Angelico|first3=B. A.|last4=de Oliveira|first4=A. M.|last5=da Silva Filho|first5=J. I.|date=2021|title=Rotary Inverted Pendulum Identification for Control by Paraconsistent Neural Network|journal=IEEE Access|volume=9|pages=74155–74167|doi=10.1109/ACCESS.2021.3080176|bibcode=2021IEEEA...974155D |issn=2169-3536|doi-access=free}}</ref>
* [[Deontic logic]] and [[metaethics]]: Paraconsistent logic has been proposed as a means of dealing with ethical and other normative conflicts.
* [[Software engineering]]: Paraconsistent logic has been proposed as a means for dealing with the pervasive inconsistencies among the [[documentation]], [[use cases]], and [[Source code|code]] of large [[software systems]].<ref name="Hewitt 2008b">Hewitt (2008b)</ref><ref name="Hewitt 2008a">Hewitt (2008a)</ref><ref>Carl Hewitt. "Formalizing common sense reasoning for scalable inconsistency-robust information coordination using Direct Logic Reasoning and the Actor Model". in Vol. 52 of ''Studies in Logic''. College Publications. {{isbn|1848901593}}. 2015.</ref>
* [[Expert system]]. The Para-analyzer algorithm based on paraconsistent annotated logic by 2-value annotations (PAL2v), also called paraconsistent annotated evidential logic (PAL ''E''t), derived from paraconsistent logic, has been used in decision-making systems, such as to support medical diagnosis.<ref>{{cite journal |last1=de Carvalho Junior |first1=Arnaldo |last2=Justo |first2=João Francisco |last3=de Oliveira |first3=Alexandre Maniçoba |last4=da Silva Filho |first4=João Inacio |title=A comprehensive review on paraconsistent annotated evidential logic: Algorithms, Applications, and Perspectives |journal=Engineering Applications of Artificial Intelligence |date=1 January 2024 |volume=127 |issue=B |pages=107342 |doi=10.1016/j.engappai.2023.107342|s2cid=264898768 }}</ref>
* [[Electronics]] design routinely uses a [[four-valued logic]], with "hi-impedance (z)" and "don't care (x)" playing similar roles to "don't know" and "both true and false" respectively, in addition to true and false. This logic was developed independently of philosophical logics.
* [[Control system]]: A model reference control built with recurrent paraconsistent neural network for a rotary inverted pendulum presented better robustness and lower control effort compared to a classical well tuned pole placement controller.<ref>{{cite journal|author1=Carvalho, A.|author2=Angelico, B. A.|author3=Justo, J. F.|author4=Oliveira, A. M.|author5=Silva, J. I. D.|title=Model reference control by recurrent neural network built with paraconsistent neurons for trajectory tracking of a rotary inverted pendulum|journal=Applied Soft Computing| year=2023|volume=133|pages=109927|issn=1568-4946|doi=10.1016/j.asoc.2022.109927}}</ref>
*[[Digital filter]]: PAL2v Filter Algorithm, using a paraconsistent artificial neural cell of learning by contradiction extraction (PANLctx) in the composition of a paraconsistent analysis network (PANnet), based on the PAL2V rules and equations, can be used as an estimator, average extractor, filtering and in signal treatment for industrial automation and robotics.<ref>{{cite journal |last1=de Carvalho Junior |first1=Arnaldo |last2=Justo |first2=João Francisco |last3=de Oliveira |first3=Alexandre Maniçoba |last4=da Silva Filho |first4=João Inacio |title=A comprehensive review on paraconsistent annotated evidential logic: Algorithms, Applications, and Perspectives |journal=Engineering Applications of Artificial Intelligence |date=1 January 2024 |volume=127 |issue=B |pages=107342 |doi=10.1016/j.engappai.2023.107342|s2cid=264898768 }}</ref><ref>{{cite book |last1=de Carvalho Jr. |first1=Arnaldo |last2=Da Silva Filho |first2=João Inácio |last3=de Freitas Minicz |first3=Márcio |last4=Matuck |first4=Gustavo R. |last5=Côrtes |first5=Hyghor Miranda |last6=Garcia |first6=Dorotéa Vilanova |last7=Tasinaffo |first7=Paulo Marcelo |last8=Abe |first8=Jair Minoro |title=Advances in Applied Logics |chapter=A Paraconsistent Artificial Neural Cell of Learning by Contradiction Extraction (PANCLCTX) with Application Examples |series=Intelligent Systems Reference Library |date=2023 |volume=243 |pages=63–79 |doi=10.1007/978-3-031-35759-6_5|isbn=978-3-031-35758-9 }}</ref><ref>{{cite journal |last1=Carvalho |first1=Arnaldo |last2=Justo |first2=João F. |last3=Angélico |first3=Bruno A. |last4=de Oliveira |first4=Alexandre M. |last5=da Silva Filho |first5=João Inacio |title=Paraconsistent State Estimator for a Furuta Pendulum Control |journal=SN Computer Science |date=22 October 2022 |volume=4 |issue=1 |doi=10.1007/s42979-022-01427-z|s2cid=253064746 }}</ref>
*[[Contradiction]] Extractor. A recurrent algorithm based on the PAL2v rules and equations has been used to extract contradictions in a set of statistical data.<ref>{{cite journal |last1=de Carvalho Junior |first1=Arnaldo |last2=Justo |first2=João Francisco |last3=de Oliveira |first3=Alexandre Maniçoba |last4=da Silva Filho |first4=João Inacio |title=A comprehensive review on paraconsistent annotated evidential logic: Algorithms, Applications, and Perspectives |journal=Engineering Applications of Artificial Intelligence |date=1 January 2024 |volume=127 |issue=B |pages=107342 |doi=10.1016/j.engappai.2023.107342|s2cid=264898768 }}</ref>
* [[Quantum physics]]
* [[Black hole]] physics
* [[Hawking radiation]]
* [[Quantum computing]]
* [[Spintronics]]
* [[Quantum entanglement]]
* [[Quantum coupling]]
* [[Uncertainty principle]]